Reflecting A Plane Electromagnetic Wave

Instructions

This applet presents the electric and magnetic fields of an incident, reflected, and transmitted plane electromagnetic wave. The incident wave is generated by clicking somewhere in the red rectangle in the upper left of the canvas and dragging up and down. This motion of the positive charges there will generate an electromagnetic wave, in the way that we have previously discussed. The incident wave then impinges on a plane in the middle of the canvas which has finite resistance, and the electric field of the incident wave then shakes the positive charges (only) there up and down. That charge motion generates a reflected and transmitted wave.

The electric field of either the incident electromagnetic wave or the total (incident plus reflected and transmitted) electromagnetic wave is indicated by the black vectors at the top of the canvas. Hitting the toggle button in the upper right will toggle between the incident electric field and the total electric field ("toggle" means everytime you hit it it changes state), with the incident field shown initially. You can vary the resistance of the middle plane from zero to large values by using the scroll bar on the upper left (see footnote for the meaning of this resistance).

After you have clicked on the red rectangle, as long as you are dragging the mouse the waves will propagate. As soon as you stop dragging the mouse, the waves stop propagating. This then gives you a snapshot of the waves you have generated up to that point, so that you can analyze what was generated at your leisure. As the incident wave propagates to the right, it eventually impinges on the plane of charge in the middle of the canvas. The electric fields of the negative and positive charges in this thin plane are shown by the green lines in the middle of the canvas. We assume that the positive charges in that plane (red box) will move up and down due to the arrival of the electric field of the impinging incident wave. We also assume that the negative charges in the middle plane (black box) are so massive that they do not move at all in this electric field. We assume that the velocity of the positive charges in the middle plane is proportional to the applied electric field, e.g., we assume that Ohm's Law holds.

The perturbation electric field generated by the motion of the positive charges in the middle plane is indicated in the bottom panel. Note that when the middle positive charges are moving up, the perturbation electric field right at the sheet that this motion generates is down, as we have seen before. Since the middle positive charges are moving up when the incident electric field is up, this means that the electric field generated by the motion of the positive charges in the middle sheet opposes the direction of the incident electric field right at the middle sheet. When this generated wave propagates away from the middle sheet, it thus tends to cancel out the incident wave to the right, and add up to give a standing wave to the left. See the notes that we have referred to previously for a complete discussion of this.

Footnote: When you vary the "Resistance of the Plane" parameter you are varying the value of two times the resistivity of the material making up the plane divided by (the speed of light times the thickness D of the plane times mu naught). (See the Appendix of the notes referenced above, particularly equation (14) and (15) on page 8.) Using the values of mu naught and the speed of light, this means that for a value of unity of the "Resistance of the Plane" parameter, the ratio of the resistivity of the plane to its thickness is 188.5 Ohms. The value 188.5 Ohms is half the "impedance of the vacuum", 377 Ohms, which is the speed of light times mu naught, and has units of Ohms. If the resistance of the middle plane defined in this way is much greater than the "impedance of the vacuum", then ohmic disspation into heat is the predominant energy loss associated with the charge motion; if the resistance of the middle plane defined in this way is much smaller than "the impedance of the vacuum" then the loss of energy due to the generation of radiation is the predominant energy loss associated with the charge motion.